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a = b if (a^2 + ab + 1) a multiple of (b^2 + ab + 1)

Source: 10th QEDMO p3 Juniors (8-10. 12. 2011) https://artofproblemsolving.com/community/c1512515_qedmo_200507

May 16, 2021
multiplenumber theorydivides

Problem Statement

Let a,ba, b be positive integers such that a2+ab+1a^2 + ab + 1 a multiple of b2+ab+1b^2 + ab + 1. Prove that a=ba = b.
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